Semitonal Pairings and the Performance of Schoenberg's Atonal Piano Music

Questions of tonal function in Schoenberg’s so-called “atonal” works have proven difficult for analysts, as they contain tonal residues that are frequently not given structural support in harmony or voice leading. Previous tonal approaches such as Von der Nüll 1932, Leichtentritt 1959, Brinkmann 1969, and Ogdon 1981 have generally favored tonal centers that are suggested by traditional major and minor scales, an approach that has overlooked rich relationships possible between tonalities and pc set structures. To link tonal and pc set structures, a promising starting point is the layering of tonalities in different registers, a flexible “polytonality” that is dealt with informally in Leichtentritt 1959. Leichtentritt implies a dialectic between two tonal layers that results in three possible types of overall harmonic states: 1) no mixture; 2) one of the two layers functions as added notes to the other layer; and 3) the two layers assert the same tonality. This paper formalizes Leichtentritt’s implied dialectic through a new model of Semitonal Pairings (SPs), sustained conflicts between layered tonalities, symmetrical collections, or intervals related by ic 1. SPs show how tonal residues are integrated into the chromatic, dissonant motivic structure of atonal works by considering a layered, polytonal texture as equivalent to the subset/superset relationship from set theory. Due to changing relationships between subset layers, the supersets range from traditionally dissonant (2 or more instances of ic 1) to relatively consonant (no instances of ic 1). Successions of these harmonic states may be interpreted as a narrative within the tradition of the Schoenbergian “tonal problem” (Schoenberg 1995) and its extensions in Carpenter 1983 and Dineen 2005. This paper will classify types of SPs, trace their different types in Schoenberg’s Op. 11 and 19, and interpret their performance implications. This approach demonstrates 1) that some (but not all) tonal centers relate to pc sets in a consistent manner, and 2) these relationships may help inform an effective performance.

Dysfunctional Diatonicism: The Use of Quartal Hamonies in Stravinsky's Pulcinella

Igor Stravinsky used many compositional techniques in transforming a disparate group of eighteenth-century works into his ballet Pulcinella. On the surface, Pulcinella appears to be a straightforward adaptation of its source materials. However, while the sources for Pulcinella operate within the norms of common practice tonality, there are many instances where Stravinsky subverts the sources’ original tonal implications. One such way is through the addition of non-functional diatonic harmonies, used in conjunction with other compositional techniques such as pedal points and dissociative layers.

Beyond the tertian harmonies that mostly come from the source materials, quartal sonorities are the most prevalent harmonic additions. They are interesting because while they can be easily created within the diatonic collection, they are seen as non-functional byproducts of voice-leading within a traditional tonal context. These quartal harmonies are discussed in an assortment of twentieth century treatises, perhaps most notably in Schoenberg’s Theory of Harmony, but also in the in the work of Hindemith, Caner, Persichetti, and Harris. Schoenberg’s reference to “quartal triads” is then extrapolated in this paper to include other pentatonic subsets.

Stravinsky’s use of quartal harmonies in the ballet is then examined. In some instances Stravinsky uses entire quartal sonorities as pedal points. Instances where quartal harmonies are used as one element of complex, layered textures will also be looked at in detail. Lastly, the end of the Tarantella will be discussed, where the combination of the aforementioned techniques and the original tonal implications conflict with how non-functional harmonies are perceived.

Two central and related features of Stravinsky’s music are his metrically displaced accents and his idiosyncratic text settings, the latter of which often result from the former. Building on Pieter van den Toorn’s long-standing work on displacement, I examine Stravinsky’s practice of displacing syllables in works spanning from the late 1910s to the early 1950s. The strict displacement that van den Toorn analyzes — in which themes, motives, and chords are retained “in order that alignment itself (and its shifts) might be set in relief” — occurs mostly in the Russian-period settings. A close examination of Stravinsky’s later displaced settings shows Stravinsky loosening his grip on pitch, rhythm and even dynamics. I propose to survey these more subtle and varied uses of displacement in the post-Russian-period text settings, including Oedipus Rex (1926-7), Perséphone (1934), The Rake’s Progress (1948-51) and Cantata (1952), the last of which spans Stravinsky’s controversial transition to serialism. Drawing on some revealing sketch material, I will show not only how Stravinsky’s approach to setting text evolves, but also how his use of displacement develops even as it remains key to his highly distinctive treatment of rhythm, meter and text. By surveying examples from many works composed over a span of years, I offer another perspective by which to gauge the striking variety and remarkable evolution of Stravinsky’s music.

The opening scene of Schoenberg’s Moses und Aron introduces four
issues that are elaborated through the opera—1) Moses’ inability to grasp
the idea of God perfectly; 2) God's continual attempts to win His argument
with Moses and convince him to prophesy; 3) the powerful effect of visual
images in representing God for good or evil, and 4) the Jews' unique status
as "chosen people” and model for other nations. Schoenberg portrays each of
these issues effectively using different transpositions and partitions of
his basic row in the first scene, and though previous authors have described
some of his depictive processes, there are still many left to illustrate.

Moses’ inability to understand God is pictured by the six singing
voices from the burning bush introducing a partition in mm. 11–15 (David
Lewin’s “X + Y”) that Moses’ music first approximates, then gradually “gets
wrong” in the measures immediately following. God’s attempts to win Moses
over give rise to passages in which the six voices take over first the
harmonic areas and then the partitions originally associated with the
reluctant prophet (mm. 26–28, 30–35, 41–47, and 53–66).

The power of visual images to represent God is depicted by gradually
allowing a “chromatic tetrachord” partition (so named by Michael Cherlin) to
take over the texture, as the voices predict the three signs Aaron will do
to convince the people that God is real (mm. 41–47). Finally, the special
status of the Hebrew people as model for the nations around them is
portrayed (in mm. 71–85) by giving correctly-ordered hexachords from P9, I0,
or their retrogrades to certain “chosen” voices, doubled by the strings, and
leaving reorderings or fragments of those same hexachords for the remaining
voices and instruments.